The motivating problem for this research concerns the angular acceleration of a stepper motor with a fixed load.
Above, we can see a simple schematic which illustrates the behavior of the stepper motor. Alternating reversals in voltage across each motor coil cause reversals in magnetic polarity which in turn cause the rotor to “step” clockwise. We model the voltage changes as discrete events dictated by a fixed, open-loop acceleration strategy. All other dynamics are continuous and given as ODEs in the paper.
An aero-astro engineer first posed the problem to me: His small satellite design team is designing a satellite that launches smaller hockey-puck shaped satellites which spin and measure the Earth’s magnetosphere. His task was to devise a fixed strategy for angular acceleration of the puck in the face of many uncertain parameters. For instance, the puck’s inertia wasn’t known because it’s design wasn’t yet complete. He provided bounds for each system parameter and wanted to know if his acceleration strategy could cause a stall for any possible set of system parameters.